The ex-Arsenal midfielder confirmed his switch to Stamford Bridge on Thursday, while Costa told Goal that his own transfer from Atletico Madrid is imminent.
|2/1||Chelsea are 2/1 with Bet365 to win the Premier League|
The centre forward told Onda Cero: "I wish [Fabregas] could have joined us a couple of years earlier.
"He is a blessing for strikers, he always looks to find that final key pass; he's the type of player Chelsea don't have."
Though Costa, who started up front ahead of Torres for Spain in Friday's 5-1 defeat to Netherlands at the World Cup, would represent a serious threat to the 30-year-old's game time at Stamford Bridge, the former Liverpool man claims that he welcomes the competition.
"People have been saying for some time that Chelsea have signed a striker and, if it's Diego, then it's very welcome," he declared.
"The level of competition at big clubs should always be very high."